1. Field of the Invention
The present invention relates to a high precision filter used in a communication field or the like. In particular, it relates to a notch filter which can control an attenuation.
2. Prior Art
FIG. 4 is a block diagram showing one example of a notch filter circuit which is used in a prior art, and shows a biquad-type second order notch filter configuration. In FIG. 4, reference numeral 1 represents an input terminal to which an input voltage Vin is inputted. Reference numerals 2 and 3 represent transconductance circuits which have transconductance values gm1 and gm2, respectively. Reference numerals 8 and 9 represent voltage buffer circuits, respectively. Reference numerals 6 and 7 represent capacitors which have capacitance values C1 and C2, respectively. Reference numeral 12 represents a ground terminal. Reference numeral 10 represents a filter output terminal from which an output voltage Vo is outputted.
The biquad filter circuit configures a notch filter. In the notch filter, supposing that transconductance values of the transconductance circuits 2 and 3 are gm1 and gm2, respectively, a transfer function H (s), which is defined as an output voltage/an input voltage, is given as follows. Where, s=jω.                                                                         H                ⁡                                  (                  s                  )                                            =                            ⁢                              Vo                /                Vin                                                                                        =                            ⁢                                                (                                                            s                      2                                        +                                          gm1                      ·                                              gm2                        /                                                  (                                                      C1                            ·                            C2                                                    )                                                                                                      )                                /                                                                                                      ⁢                              (                                                      s                    2                                    +                                      s                    ·                                          (                                              gm2                        /                        C2                                            )                                                        +                                      gm1                    ·                                          gm2                      /                                              (                                                  C1                          ·                          C2                                                )                                                                                            )                                                                        (        1        )            
Here, one example of a specific circuit configuration of the transconductance circuit 2 is shown in FIG. 10. The transconductance circuit 3 has a similar circuit configuration, and a transconductance circuit which is added in a below-mentioned embodiment (refer to FIG. 1) also has a similar circuit configuration. In FIG. 10, reference numeral 2A represents a positive polarity input terminal, reference numeral 2B represents a negative polarity input terminal, reference numeral 2C represents an output terminal, reference numerals M1, M2, and M3 represent MOS transistors, respectively, and reference numerals IA1 and IA2 represent current sources, respectively. Reference numeral Vdd represents a supply voltage (reference voltage) applied to the transconductance circuit, and reference numeral Vc represents a control voltage applied to the transconductance circuit.
The MOS transistors M1, M2, and M3 configure the transconductance. Supposing that a current which flows through the MOS transistor M3 is 2Io and a gain constant is β, the transconductance value gm1 is expressed as follows.gm1=(βIo/2)1/2Where, the gain constant β is represented as follows.β=μCox(W/L)Here, a symbol μ represents mobility, a symbol Cox represents a gate oxide capacitance, a symbol W represents a gate width, and a symbol L represents a gate length.
Accordingly, a value of the transconductance value gm1 can be controlled by controlling the gate voltage Vc of the MOS transistor M3.
FIG. 6 is a block diagram showing another example of a second order notch filter of the prior art. In FIG. 6, reference numeral 1A represents a positive phase filter input terminal to which an input voltage Vin/2 is inputted, and reference numeral 1B represents a negative phase filter input terminal to which an input voltage −Vin/2 is inputted. Reference numerals 20, 30, 13, and 14 represent full differential transconductance circuits that have transconductance values gm1, gm2, gm5, and gm6, respectively. Reference numerals 60, 71, and 72 represent capacitors which have capacitance values C1, C21, and C22, respectively. Reference numerals 10A and 10B represent a positive phase filter output terminal and a negative phase filter output terminal from which an output voltage Vo is outputted, respectively.
Then, a filter output is derived from between the positive phase filter output terminal 10A and the negative phase filter output terminal 10B, and a notch filter of a full differential type is configured.
Supposing that the transconductance values of the full differential transconductance circuits 20, 30, 13 and 14 are gm1, gm2, gm5, and gm6, respectively, the capacitance values of the capacitors 71 and 72 are C21 and C22, respectively, and C21=C22=2C2, a transfer function H (s) between the positive phase filter output terminal 10A and the negative phase filter output terminal 10B defined as the output voltage/the input voltage is given as follows. Where, s=jω.                                                                         H                ⁡                                  (                  s                  )                                            =                            ⁢                              Vo                /                Vin                                                                                        =                            ⁢                                                (                                                            s                      2                                        +                                          gm1                      ·                                              gm6                        /                                                  (                                                      C1                            ·                            C2                                                    )                                                                                                      )                                /                                                                                                      ⁢                              (                                                      s                    2                                    +                                      s                    ·                                          (                                              gm2                        /                        C2                                            )                                                        +                                      gm5                    ·                                          gm6                      /                                              (                                                  C1                          ·                          C2                                                )                                                                                            )                                                                        (        2        )            
Here, one example of a specific circuit configuration of the transconductance circuit 20 is shown in FIG. 11. The transconductance circuits 30, 13, and 14 have a similar configuration, and a transconductance circuit which is added in a below-mentioned embodiment (refer to FIG. 2 and FIG. 3) also has a similar configuration. In FIG. 11, reference numeral 20A represents a positive polarity input terminal, reference numeral 20B represents a negative polarity input terminal, reference numeral 20C represents a positive polarity output terminal, and reference numeral 20D represents a negative polarity output terminal. Reference numerals M11, M12, and M13 represent MOS transistors, respectively. Reference numerals IB1 and IB2 represent current sources, respectively. Reference numeral Vdd represents a supply voltage (reference voltage) applied to the transconductance circuit, and reference numeral Vc represents a control voltage applied to the transconductance circuit.
MOS transistors M11, M12, and M13 configure the transconductance. Supposing that a current which flows through the MOS transistor M13 is 2Io and a gain constant is β, the transconductance value gm1 is expressed as follows.gm1=(βIo/2)1/2Where, the gain constant β is represented as follows.β=μCox(W/L)Here, a symbol μ represents mobility, a symbol Cox represents a gate oxide capacitance, a symbol W represents a gate width, and a symbol L represents a gate length.
Accordingly, the value of transconductance value gm1 can be controlled by controlling the gate voltage Vc of the MOS transistor M13.
FIG. 8 is a block diagram showing one example of a second order all-pass filter of the prior art. In FIG. 8, reference numeral 17 represents an operational amplifier and the operational amplifier 17 configures an inverting amplifier. Reference numerals 15 and 16 represent resistors which have resistance values R2 and R2′, respectively. Reference numerals 600 and 700 represent capacitors which have capacitance values C1 and C2, respectively. Reference numeral 12 represents a ground terminal, reference numeral 1C represents a signal input terminal to which an input voltage Vin is inputted, and reference numeral 10C represents a signal output terminal from which an output voltage Vo is outputted. Reference numerals 200 and 300 represent transconductance circuits, which are amplifiers having transconductance values gm1 and gm2, respectively. Reference numerals 80 and 90 represent voltage buffer circuits, respectively.
Supposing that transconductance values of each of the transconductance circuits 200 and 300 are gm1 and gm2, respectively, the output of the operational amplifier 17 of the filter circuit shows all-pass filter characteristics. A transfer function H (s) of the operational amplifier 17, which is defined as an output voltage/an input voltage thereof is given as follows. Where, s=jω and R2=R2′.                                                                         H                ⁡                                  (                  s                  )                                            =                            ⁢                              Vo                /                Vin                                                                                        =                            ⁢                              -                                  (                                                            s                      2                                        -                                          s                      ·                                              gm2                        /                        C2                                                              +                                                                  (                                                  gm1                          ·                                                      gm2                            /                                                          (                                                              C1                                ·                                C2                                                            )                                                                                                      )                                            /                                                                                                                                                            ⁢                              (                                                      s                    2                                    +                                      s                    ⁡                                          (                                              gm2                        /                        C2                                            )                                                        +                                      gm1                    ·                                          gm2                      /                                              (                                                  C1                          ·                          C2                                                )                                                                                            )                                                                        (        3        )            
As for an active filter which has used the operational amplifier, and a filter which has used the transconductance circuit, deviation from target characteristics has often occurred. The cause is that the amplifier or the transconductance circuit generally has a finite gain or finite frequency characteristics; namely, there exists the deviation from the ideal characteristics. In particular, in a steep filter having high selectivity, or a notch filter having a large attenuation, the deviation has become larger, and that has made it difficult to realize the characteristics.
A notch filter, in which a finite parasitic output resistor 11 is added to the transconductance circuit 2, is shown in FIG. 5. Supposing that a resistance value of the output resistor 11 of the transconductance circuit 2 is RL and others are similar to those of FIG. 4, a transfer function H(s) of the notch filter is given as follows.                                                                         H                ⁡                                  (                  s                  )                                            =                            ⁢                              Vo                /                Vin                                                                                        =                            ⁢                                                (                                                            s                      2                                        +                                          s                      /                                              (                                                  C1                          ·                          RL                                                )                                                              +                                          gm1                      ·                                              gm2                        /                                                  (                                                      C1                            ·                            C2                                                    )                                                                                                      )                                /                                                                                                      ⁢                              (                                                      s                    2                                    +                                      s                    ·                                          (                                                                        1                          /                                                      (                                                          C1                              ·                              RL                                                        )                                                                          +                                                  gm2                          /                          C2                                                                    )                                                        +                                                                                                                      ⁢                                                (                                      gm1                    +                                          1                      /                      RL                                                        )                                ·                                  gm2                  /                                      (                                          C1                      ·                      C2                                        )                                                              )                                                          (        4        )            
As can be seen from equation (4), a primary term is left in a numerator of the transfer function H (s).
Here, when the resistance value RL is infinite, it becomes the same value as equation (1), but generally, since the resistance value RL is finite, the depth of the notch is not a infinite value but a finite value. In addition, a characteristic frequency or selectivity also deviates from ideal characteristics. The resistor 11 which has the resistance value RL is a phase advance element to the integrator.
In addition, supposing that the resistance value RL is infinite, approximating that only the frequency characteristics of the transconductance value gm1 is that of a primary low pass filter, and defining that a transfer function thereof is G(s)=ωa/(s+ωa), the transfer function of the notch filter H (s) can be approximated as follows.                                                                         H                ⁡                                  (                  s                  )                                            =                            ⁢                              Vo                /                Vin                                                                                        =                            ⁢                              (                                                      s                    2                                    -                                                            s                      ⁡                                              (                                                                              gm1                            ·                                                          gm2                              /                                                              (                                                                                                      C1                                    ·                                    C2                                    ·                                    ω                                                                    ⁢                                                                                                                                           ⁢                                  a                                                                )                                                                                                              +                                                      gm1                            ·                                                          gm2                              /                                                              (                                                                  C1                                  ·                                  C2                                                                )                                                                                                                                    )                                                              /                                                                                                                                        ⁢                              (                                                      s                    2                                    +                                      s                    ·                                          (                                                                        gm2                          /                                                      (                                                          C2                              -                                                              gm1                                ·                                                                  gm2                                  /                                                                      (                                                                                                                  C1                                        ·                                        C2                                        ·                                        ω                                                                            ⁢                                                                                                                                                           ⁢                                      a                                                                        )                                                                                                                                                        )                                                                          +                                                                                                                                                                                  ⁢                              (                                  gm1                  ·                                      gm2                    /                                          (                                              C1                        ·                        C2                                            )                                                                      )                                                                        (        5        )            
Accordingly, similar to equation (4), the primary term is left in the numerator of the transfer function H (s), and the attenuation does not become infinite unless the angular frequency ωa is infinite.
An example of the characteristics of the integrator which consists of the conductance gm1, the capacitance C1, and the resistance RL is shown in FIG. 7. In FIG. 7, a gain and a phase substantially begin to change from a first pole which is determined by the capacitance C1 and the resistance RL, and begin to change once again at a second pole which is determined by the frequency characteristics of the transconductance circuit. Accordingly, depending on which frequency on the characteristics of the integrator is used, it is used as a phase lag or phase advance integrator. Incidentally, a turning point of the gain is a turning point of the pole, and the phase changes from 0 to −90 degrees at the first pole.
Ideally, although the phase of the integrator should not be based on the frequency but must be constant at −90 degrees, in the frequency fA shown in the example of FIG. 7, it will be used in a state of a slight phase lag, thereby the filter characteristics deviate from the target.
One countermeasure implemented to this is inserting a resistance r in series with the capacitance C1 to perform a phase compensation similar to the phase compensation of the operational amplifier or the like as described by Yannis P. Tsividis, “Integrated Continuous-Time Filter Design-An Overview” IEEE Journal of Solid-State Circuits, Vol. 29, No3, March 1994, PP 166-173.
Generally, the value of the resistance r is chosen near ωa=1/(C1·r).
However, when the transconductance circuit which comprises of a transistor is compensated by a pure resistance, a problem that it is weak against variations in elements arises, and it cannot be used for a phase advance element.
For this reason, it has been difficult to deliver sufficient characteristics in a notch filter particularly sensitive to the change in phase. In addition, similarly, an all-pass filter has had a constant gain and has been intended to use the only change in phase, a similar problem has been existed.
A characteristics chart, such as a notch filter, is shown in FIG. 9. In FIG. 9, by a non-ideal effect of the transconductance circuit or the operational amplifier, originally, in FIG. 9, even when characteristics as shown in reference numeral (a) have been a target, as shown in reference numeral (b) in the same figure, it may become notch characteristics having insufficient attenuation. In addition, even when the all-pass filter which has characteristics as shown in reference numeral (c) of the same figure is a target, it may become a filter which has characteristics as shown in reference numeral (b) or reference numeral (d) of the same figure by the non-ideal effect of the transconductance circuit or the operational amplifier.